Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems

A. I. Levykin, A. E. Novikov, E. A. Novikov

Research output: Contribution to journalArticlepeer-review


A form of Rosenbrock-type methods optimal in terms of the number ofnon-zero parameters and computational costs per step is considered. Atechnique of obtaining (m, k) -methodsfrom some well-known Rosenbrock-type methods is justified. Formulas fortransforming the parameters of (m, k) -schemesand for obtaining a stability function are given for two canonicalrepresentations of the schemes. An L-stable(3 , 2) -methodof order 3 is proposed, which requires two evaluations of the function:one evaluation of the Jacobian matrix and oneLU-decompositionper step. A variable step size integration algorithm based on the(3 , 2) -methodis formulated. It provides a numerical solution for both explicit andimplicit systems of ODEs. Numerical results are presented to show theefficiency of the new algorithm.

Original languageEnglish
Pages (from-to)34-44
Number of pages11
JournalNumerical Analysis and Applications
Issue number1
Publication statusPublished - 25 Feb 2020


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